If you pay online in advance, it will cost you $30 to stow your carry-on in an overhead bin, but if you wait until you get to the gate, it will cost $45. Passengers may still place one personal item under the seat in front of them, free of charge.

The new carry-on fee went into effect Monday and applies to flights booked for Aug. 1 or later. Fliers who pay in advance for their carry-on luggage will be the first to board the airplane, Spirit said.

"In addition to reducing fares even further, this will reduce the number of carry-on bags, which will improve inflight safety and efficiency by speeding up the boarding and deplaning process, all of which ultimately improve the overall customer experience," Chief Operating Officer Ken McKenzie said in a statement.

At the same time, Spirit will lower fees for checked luggage. Spirit Airline members will pay $15 for their first and second bags if they pay online, instead of the $19 and $25 that was previously charged. Non-members, however, will pay more: The first bag is $25 online and $45 at the airport; $30 for the second bag.

While many other airlines also charge for checked luggage, they still allow passengers to stow carry-on luggage for free.

David Castelveter, a spokesman at Air Transport Association, which represents the leading U.S. airlines, said he's not aware of any ATA members charging for carry-on luggage.

JetBlue (JBLU) lets passengers bring a carry-on bag as well as a personal item aboard with no extra fee. Customers are also able to check their first bag for free, but a second checked bag costs $30.

Other major airlines, including Delta (DAL, Fortune 500), Continental (CAL, Fortune 500), Frontier and United, all let passengers carry on one bag and one personal item for free, but charge fliers around $20 for the first checked bag and $30 for the second.